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A commutative algebra, function theory, and system of analysis is developed for one 4-D variable (not quaternions). It is based upon a commutative group ring and extends all of the properties of the classical complex variables.
A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.
A simple review of the powerful technique of dimensional analysis.
A brief introduction to the properties and uses of the Dirac delta function. [PDF]
A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.
A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
Lecture notes from the ITP miniprogram on Geometry and Duality
This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations.
These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
Relationships between number theory and physics.
Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.
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